Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-200.2-a
Conductor 200.2
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{-1}) \)

Generator \(i\), with minimal polynomial \( x^{2} + 1 \); class number \(1\).

Elliptic curves in class 200.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 200.2-a contains 10 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
200.2-a1 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -31 i - 44\) , \( 94 i + 106\bigr] \)
200.2-a2 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 30 i - 44\) , \( -138 i + 76\bigr] \)
200.2-a3 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -4\) , \( -6 i\bigr] \)
200.2-a4 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 60 i - 34\) , \( 14 i + 180\bigr] \)
200.2-a5 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -61 i - 34\) , \( -48 i + 240\bigr] \)
200.2-a6 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 1\) , \( i\bigr] \)
200.2-a7 \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
200.2-a8 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 26\) , \( 66 i\bigr] \)
200.2-a9 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 480 i - 694\) , \( -7778 i + 5556\bigr] \)
200.2-a10 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -481 i - 694\) , \( 7084 i + 6036\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 4 & 2 & 8 & 2 & 4 & 8 & 8 & 8 & 2 \\ 4 & 1 & 2 & 2 & 8 & 4 & 8 & 8 & 2 & 8 \\ 2 & 2 & 1 & 4 & 4 & 2 & 4 & 4 & 4 & 4 \\ 8 & 2 & 4 & 1 & 16 & 8 & 16 & 16 & 4 & 16 \\ 2 & 8 & 4 & 16 & 1 & 8 & 16 & 16 & 16 & 4 \\ 4 & 4 & 2 & 8 & 8 & 1 & 2 & 2 & 8 & 8 \\ 8 & 8 & 4 & 16 & 16 & 2 & 1 & 4 & 16 & 16 \\ 8 & 8 & 4 & 16 & 16 & 2 & 4 & 1 & 16 & 16 \\ 8 & 2 & 4 & 4 & 16 & 8 & 16 & 16 & 1 & 16 \\ 2 & 8 & 4 & 16 & 4 & 8 & 16 & 16 & 16 & 1 \end{array}\right)\)

Isogeny graph